Regularization Extragradient Method for Lipschitz Continuous Mappings and Inverse Strongly-Monotone Mappings in Hilbert Spaces

The purpose of this paper is to present a regularization variant of the extragradient method for finding a common element of the solution sets for a variational inequality problem involving a $\tilde k$-Lipschitz continuous monotone mapping $A$ and for a finite family of $\lambda_i$-inverse strongly-monotone operators $\{A_i\}^N_{i=1}$ from a closed convex subset $K$ into the Hilbert space $H$.